A characterization of some simple unitary groups via order and degree pattern of solvable graph

Abstract

The solvable graph associated with a finite group $G$, denoted by ${Gamma}_{rm s}(G)$, is a simple graph whose vertices are the prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge if and only if there exists a solvable subgroup of $G$ whose order is divisible by $pq$. In this paper, we give a<br />characterization for projective special unitary groups $U_3(q)$ with some certain conditions by the solvable graph.